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Question

The potential energy U in joule of a particle of mass 1 kg moving the x-y plane obeys the law U = 3x + 4y, where (x, y) are the co-ordinates of the particle in meter. If the particle is at rest at (6, 4) at time t = 0 then:


A

The particle has constant acceleration

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B

The particle has zero acceleration

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C

The speed of the particle when it crosses y-axis is 10 m/s

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D

Co-ordinate of particle at t = 1 sec is (4.5, 2)

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Solution

The correct options are
A

The particle has constant acceleration


C

The speed of the particle when it crosses y-axis is 10 m/s


D

Co-ordinate of particle at t = 1 sec is (4.5, 2)


(A) Fx=dUdx=3
Fy=dUdy=4F=(3^i+4^j)N
(C) For particle to cross y-axis x = 0
x=vxt+12axt26=012×3t2t=2 sec
For resultant velocity
v=0(3i+4j)×2|v|=10 m/s

(D) Δx=012×3×12=1.5Δy=012×4×12=2
Co - ordinate = (6 - 1.5, 4 - 2) = (4,5,2)


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